Use our free GCF of Fractions Calculator tool to compute the GCF of 76/624, 42/306, 715/232 i.e 1/922896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 76/624, 42/306, 715/232.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 76/624,42/306,715/232
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 76/624,42/306,715/232, numerators are 76,42,715
Denominators are 624,306,232
The GCF of 76,42,715 is 1 .
LCM of 624,306,232 is 922896.
The greatest common factor of 76/624,42/306,715/232 = [GCF of 76,42,715]/[LCM of 624,306,232]= 1/922896
Therefore, the GCF of 76/624,42/306,715/232 is 1/922896.
To find the highest common factor of 76,42,715, we have to find the factors of both numbers and list the highest common factor.
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 715 are 1, 5, 11, 13, 55, 65, 143, 715
The HCF of 76,42,715 is 1.
Lets's calculate GCF of 76,42,715
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 715
:1,5,11,13,55,65,143,715
Greatest Common Factor
We found the factors 76,42,715 . The biggest common factor number is the GCF number.
So the greatest common factor 76,42,715 is 1.
Lets's calculate LCM of 624,306,232
2 | 624, 306, 232 |
2 | 312, 153, 116 |
2 | 156, 153, 58 |
3 | 78, 153, 29 |
26, 51, 29 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 26 x 51 x 29 = 922896
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/922896
Therefore, the GCF of Fractions 76/624,42/306,715/232 is 1/922896
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 624,306,232 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(624,306,232) = 2
common factors(in case of two or more numbers have common factors) = 24
GCF(624,306,232) x common factors =2 x 24 = 48
LCM(624,306,232) = ( 624 × 306 × 232 ) / 48
LCM(624,306,232) = 44299008 / 48
LCM(624,306,232) = 922896
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 76,42,715?
The HCF of 76,42,715 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 76/624, 42/306, 715/232?
Answer: GCF of Numerators as per given numbers 76/624, 42/306, 715/232 is
GCF of Numerators i.e. for 76,42,715 is 1
LCM of denominators i.e. for 624,306,232 is 922896.
Thus, GCF of Fractions is 1/922896.Finally, GCF of Fractions for 76/624, 42/306, 715/232 is 1/922896.